Predicting Neural Scaling Laws without Training: A Data Manifold Oracle

Neural scaling laws set large-scale pretraining budgets, yet estimating a data scaling exponent requires fitting dozens of compute-intensive proxy models, one sweep per candidate corpus. We propose the Data Manifold Oracle (DMO), a training-free framework that predicts neural data scaling trajectories directly from the static, lossless compression properties of raw text. By linking the sequence-length scaling behavior of DEFLATE compression to neural loss decay, DMO forecasts the data scaling exponent ${\alpha }_D$ before any model is trained on the candidate corpus. We pair that predictor with a theoretical boundary: symbol-level compressibility cannot uniquely resolve the dimension of a continuous source, at any sample size. A calibration frozen on $38$ pretraining corpora predicts the exponents of five held-out corpus families to an MAE of $0.029$ without GPU overhead, against $0.084$ for a proxy model trained on the candidate corpus itself. By turning scaling law estimation from a multi-GPU training challenge into a data-profiling task, DMO makes each additional candidate corpus cost one compression pass instead of one training sweep.